A pair of bevel gears is mounted on two intersecting shafts who have a shaft angle of 80°. The gear ratio of the gears is 1/3. Find the pitch angles.

A pair of bevel gears is mounted on two intersecting shafts who have a shaft angle of 80°. The gear ratio of the gears is 1/3. Find the pitch angles. Correct Answer 62.76°, 17.24°

θ = 80°, wg/wp = 1/3 tan yg = ((sin θ)/((wg/wp)+cos θ)) = ((sin 80°)/((1/3)+cos 80°)) = 1.94 yg = 62.76° tan yp = ((sin θ)/((wp/wg)+cos θ)) = ((sin 80°)/((3)+cos 80°)) = 0.31 yp = 17.24° We can confirm this by checking that yg + yp = θ = 80°.

Related Questions

Statement (I): Two  non-intersecting and non-parallel, i.e., non-coplanar, shafts connected by gears are called skew-bevel gears or spiral gears, and this type of gearing has a line contact the rotation of which about the axes generates the two hyperboloid pitch surfaces. Statement (II): A hyperboloid is a 3D surface formed by revolving a straight line about an axis (not in the same plane), such that every point on the line remains at a constant distance from the axis.